an asymmetric (e.g. public-key) cryptosystem, based on modular exponentiation with big exponents and modulus. RSA can be used both for signature and encryption.

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How do we guarantee plaintext is coprime in RSA?

The specifications for RSA state: $P^{\phi(N)} \equiv 1 ~mod~N$ if and only if $P$ and $N$ are coprime. Here $P$ is the plaintext and $N$ is the product of two suitable primes $x_1, x_2$. My question ...
1
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1answer
173 views

Why doesn't this defeat RSA?

Apologies for the obviously ridiculous question but I need to know where I'm going wrong here. For RSA, we compute $n=pq$ for primes $p$ and $q$. We then choose an $e$ such that $gcd(e, ...
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1answer
296 views

Timelock puzzle improvment

I came across this question with this answer about a cryptographic timelock-puzzle that needs approximately 30 years to be solved. There is also an explanation with source code for that puzzle ...
2
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2answers
735 views

Computing p and q from private key

We are given n (public modulus) where n=pq and e (encryption exponent). Then I was able to crack the private key d, using Wieners attack. So now, I have (n,e,d). My question is, is there a way to ...
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3answers
68 views

with RSA encryption, how do I find the md5sum of the private key from the public key?

This is a purely mathematical question on RSA encryption. Having $e$ as the public key exponent and $n$ the modulus of a public key. Can I recover the md5sum of the private key $d$ (inverse of $d$ ...
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4answers
872 views

How do institutions like banks do RSA with big primes?

When encrypting with RSA it is often infeasible to decrypt by just doing c^d mod n, because for example when using the primes $(p,q)=(12553,1233)$, which are small ...
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1answer
97 views

RSA: How to calculate the private exponent?

I have this problem: In RSA algorithm considering $n=33$ (modulus) and public exponent $e=3$, calculate the corresponding private exponent $d$. I know that $d = e^{-1} \pmod{\varphi(n)}$ and ...
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1answer
222 views

How to create a PEM file for storing an RSA key?

I have an RSA private key $\{d,n\}$ and a public key $\{e,n\}$, where $n$ is the modulus, and I also have the prime factors $p$ and $q$ of $n$. I want to create a PEM file containing this ...
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79 views

If someone had a list of all primes, would it be possible for them to factor any integer in polynomial time? [duplicate]

For example, if they somehow got a function that would churn out any arbitrary amount of primes in a row. Could they break the RSA problem then?
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2answers
84 views

Is it hard to recover $p$ from $k \phi(p)$?

Given $k\phi(p)$, is it hard to recover $p$? Here, $p$ is a large prime, $\phi(\cdot)$ is Euler's totient function and $k$ is an unknown integer. Or what's the complexity to recover $p$ from $k ...
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0answers
89 views

How do I prove IND-CPA security of RSA-OAEP?

How do I prove that RSA-OAEP is IND-CPA secure? It would be very good to show how to prove it formally, but an informal proof would also be enough. Because of the random number in RSA-OAEP, RSA gets ...
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2answers
1k views

Is ECB mode safe to use with RSA encryption? [duplicate]

Firstly, bear with me, I'm relatively new to cryptography. In a recent static analysis scan of our application, one of the findings complained that we are using ECB: A mode of operation of a block ...
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0answers
42 views

trying to get calculator and RSA calculatin does not make sense [duplicate]

got two question, I am novice in the area of crypto and currently in big learning curve. From crypto book I am going over with, I see the RSA algorithm example as follows: it chose two rand #-s: ...
3
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2answers
298 views

Key space vs Cardinality of 1024-bit RSA

I have been trying to figure out the encryption key space, and cardinality of 1024-bit RSA. From my understanding, the key generated from 1024-bit will be primes greater than $2^{1023}$ but less than ...
0
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1answer
167 views

RSA: Why must e be relative prime to phi(n) [duplicate]

I've got a question concerning fields used in RSA: Let's use the following symbols for my example: {p,q} = primes {e,n} = public key {d,n] = private key I learnt that an inverse element exists if a ...
2
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2answers
2k views

phi(P*Q) = (P-1) * (Q-1)

I was trying to understand RSA when I encountered the Euler Function. I do understand this: $\phi(P)$, where $P$ is a prime is $P-1$. However it seems that for a number $N$ such at $N=P\cdot Q$ where ...
2
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1answer
84 views

Retrieve value of private key after encryption with the public key

Is there a way to find an RSA private key after it is encrypted with the corresponding public key? Does there exist an algorithm to recover the private key in this special case?
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1answer
85 views

Knowing N and a relationship between the 2 prime numbers(p and q) find p and q generated with RSA

Let there be $p$ and $q$, 2 prime numbers for which the following relationship is true: $|p-q| < 2 \cdot N^{1/4}$. The algorithm first generates the prime number $p$, then it generates $q$ close ...
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1answer
260 views
4
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224 views

Factoring two RSA modulus with known $|p_1 - p_2| < \ell $

I have two 1024bit RSA modulus $N_1 = p_1q_1$ and $N_2 = p_2q_2$ such that $0 <|p_1 - p_2| < \ell$, and $\ell$ is at most 64bit integer. Can I factorise $N_1$ and $N_2$? What's the answer when ...
2
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1answer
321 views

How multiplicative property of RSA can be exploited

It is known that RSA has the multiplicative property $E(m_1) \cdot E(m_2) = E(m_1 \cdot m_2)$ because $m_1^e \cdot m_2^e = (m_1 \cdot m_2)^e \pmod n$ But how can this property be used to break ...
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1answer
159 views

What use is the signature without the message under RSA?

Using RSA for signing & verification, is there a way to take a valid signature for an unknown message, and for someone else to generate a valid signature using a different key against the valid ...
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1answer
3k views

How to decrypt a '.enc' file that has been encrypted with RSA using a public key? [closed]

While solving a CTF challenge online, I came across a situation where I needed to decrypt a '.enc' file that has been encrypted using someone's public key. The ...
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1answer
788 views

Decrypted RSA 64 bit encryption using modulus and private exponent. Got gobbledygook [Verify] [closed]

As part of an experiment, I was given a .enc RSA (encrypted) file that was most likely generated using openssl. I had the public key, I factored it, obtained the private exponent, and decrypted the ...
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2answers
464 views

Toy public/private key example open to frequency analysis?

I've been looking at an online Public Key Encryption Example (summarized below). It seems to me that choosing cyphertext = plaintext^(key) mod n would produce the ...
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1answer
37 views

Identification by RSA

Suppose we have identification scheme as such: Bob takes random $r$, and encrypts it with Alices public RSA key $(n,e)$, sends $r^e$ to Alice. Alice decrypts $r$ and sends it back to Bob, becomes ...
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82 views

Asymmetric sign in public enviroment

I have RTS game, where all players run game and server just relays messages. Game can generate and store text file on player pc. I want to allow some players to be moderators, so I need to sign or ...
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3answers
713 views

How can mega store my login details and still be secure?

I understand how Mega's encryption works. For a quick summary of all those in the future looking for an answer on this... here is how it works: Upon first signing up for an account you make a ...
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1answer
164 views

Openssl library problem

I'm using openssl library and I've a problem with RSA_private_encrypt() and RSA_public_decrypt(). I'm using a key size of 256 bit with no padding of the input message. I've noted that when my input ...
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2answers
81 views

Would the Fiat Shamir identification scheme be more secure if I design it with an exponents higher than 2?

Let's say both Prover and Verifier would use nth power instead of 2nd when creating public keys and when verifying. I know it would slow it down but would that cause the protocol to be more secure?
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RSA, proof of correct work, if p is not a prime number [duplicate]

Is there any proof of correct work of RSA algorithm, if p is not a prime number? For example: n = p*q, p = p1*p2, where p1 and p2 are primes. Edit: I found that it's called Multiprime RSA, but i ...
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RSA: If I know n, e, p, and q, how do I calculate d using the extended euclidean algorithm? [duplicate]

After doing a good amount of research, it's become fairly obvious that I ought to be using the extended Euclidean algorithm to calculate d from the data that I already have. However, this isn't an ...
0
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1answer
79 views

RSA weak padding

Suppose to have a function for numbers expressed in 8-bit $\in [0,2^8-1]$ defined as: $$f(x)=x||x||x||x$$ where $|f(x)|$ is exactly 32 bits. e.g., suppose x=2 (00000010) so ...
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2answers
374 views

Practical Attack on RSA

Currently I am designing an RSA based application, and I am thinking of how long should the key be in order to be secure against attacks. I know that RSA 4096 bit key can be recovered using Sound ...
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Encrypting small values with RSA private key

I'm looking for best practices when it comes to encrypting small (< 128 bytes) amounts of data with the RSA private key. Signing it would make the resulting payload too large.
2
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1answer
478 views

Deterministically generate a RSA public/private key pair from a passphrase (with sufficient entropy)?

Is it possible to deterministically generate public/private RSA key pairs from passphrases? Would giving the (key generating) algorithm data made from key-stretching the passphrase (instead of a ...
10
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4answers
1k views

Why are RSA key sizes almost always a power of two?

I know that other bit sizes are possible, e.g. this HTTPS server seems to have a 9000 bit key https://www.ssllabs.com/ssltest/analyze.html?d=qqq.gg, but it's very rare that one sees a key not of size ...
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0answers
31 views

Practical strength of non-2^n RSA key lengths [duplicate]

It has for many years been popular to use RSA keys that have lengths that are powers of two. E.g. 1024-bit, 2048-bit and 4096-bit key lengths are all popular for use with OpenPGP implementations such ...
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35 views

I was wondering if RSA is an homomorphic crypto system? [duplicate]

I was wondering if RSA is homomorphic and how secure is it. I have read there is a variable of this but i don't fully understand the mathematics.
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29 views

Is RSA-OAEP secure when e=3? [duplicate]

Is RSA-OAEP secure when the exponent is equal to 3?
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61 views

Requested to encrypt data with AES256, digital certification, timestamped

at my job we have been tasked by gov to encrypt some data we send to them. The "law" says we have to do the title above, but they only need us to do the AES256 thing because the data is not really ...
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1answer
751 views

decrypt a saml 2.0 response having aes 128 and rsa [closed]

I need to decrypt a saml 2.0 response. But, the response object has reference to aes 128 and rsa algorithms, and I am having hard time in finding a way to decrypt. Below is the structure of the ...
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1answer
75 views

RSA Decryption from samples

I am working on a project for a client which involves decryption of data which was encrypted using RSA. The system in question retains three independent copies of each data-set, but each copy is ...
3
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1answer
559 views

RSA key pair generation and FIPS 140-2, 186-4

I need to securely generate RSA key pair and I need to have access to private exponent in order to process it further. What's the difference in FIPS 140-2 and FIPS 186-4 in connection with RSA key ...
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208 views

Java RSA Padding: no libraries used

I'm trying to implement RSA without using any java libraries using the algorithm from wikipedia HERE So, anyone can clearly see that it is a raw RSA, and can directly be attacked. The question is ...
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181 views

Why is this a fix to Bleichenbacher's attack?

Looking at the excellent explaination of the attack here: Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5? I have one additional question: It says that: ""To prevent this attack, SSL ...
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1answer
94 views

RSA padding confusion attacks

Server A produces signed messages on request. You can tell server A what type of RSA padding to use in the signature (either RSASSA-PKCS1v1_5 or RSASSA-PSS). Either way, the message will be signed ...
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1answer
125 views

Fault encryption attack on RSA [duplicate]

How to recover plaintext, if we know public key(RSA), correctly encrypted text and text encrypted with faulty public key, where one bit is changed?
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68 views

Is the half-homomorphic property of RSA a problem for blind RSA signatures?

For blind RSA signatures, is it problematic that RSA is half-homomorph? Take a scenario where blind RSA signatures are used for something like a voting procedure or this proposal: Lots of people, ...
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How does RSA signature verification work?

I understand how the RSA algorithm works for encryption and decryption purposes but I don't get how signing is done. Here's what I (think) I know and is common practice: If I have a message that I ...